COOP$^2$: Defining, Observing, and Repairing Cooperation in LLM Multi-Agent Systems

Many complex tasks require extended effort, diverse capabilities, or coordinated actions beyond what a single agent can provide. However, simply adding more agents does not guarantee better performance, as effective cooperation depends on how agents interact with each other and with task structure to satisfy evolving constraints over time. This challenge is amplified for LLM-based multi-agent systems (LLM-MAS): plans, messages, and revisions occur in natural language, whereas task progress depends on grounded environment actions. Current evaluations mostly treat cooperation as an implicit ingredient of final task success, leaving both cooperation and the effect of multi-agent interaction on task dynamics difficult to study. We introduce COOP$^2$, an evaluation framework that grounds high-level agent cooperation dynamics in LLM-MAS within task progress in the environment. COOP$^2$ then defines cooperative tasks with verifiable cooperative requirements, allowing us to analyze how cooperation unfolds over time with respect to task progress, as well as where and why cooperation breaks down. Building on this framework, we develop COOP$^2$-Repair, which predicts constraint failures from group plans and opens targeted repair channels for guided revisions. Across two environments and three communication structures, COOP$^2$-Repair improves task success and constraint satisfaction while exposing the additional decision overhead and communication load required for repair.